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Lieb-Thirring Inequalities for Quantum Systems with Inverse Nearest-Neighbor Interactions

A kinetic-energy lower bound of Lieb-Thirring type for many-body quantum systems whose particles interact through a potential equal to the inverse square of each particle's nearest-neighbor distance, with a fractional-Laplacian kinetic operator. It matches the strength of the fermionic Lieb-Thirring inequality without assuming anti-symmetric wave functions, extends to the Hardy-Lieb-Thirring inequality, and gives the asymptotics of the optimal constants in the strong-coupling limit.